This brief is concerned with studying the delay-dependent state estimation problem of recurrent neural networks with time-varying delay. The neuron activation function is more general than the sigmoid functions, and the time-varying delay is allowed to vary fast with time. A scaling parameter based approach is proposed, and a delay-dependent criterion is derived under which the resulting error system is globally asymptotically stable. It is shown that the design of a proper state estimator is directly accomplished by means of the feasibility of a linear matrix inequality. Thanks to the introduction of a scaling parameter, the developed result can efficiently be applied to chaotic delayed neural networks.